update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fsb.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
index 30864de708b70a47be1290b9054be9cc21b14092..3f4ccd360a0e953f202d6b6fec77b0f48757b690 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
@@ -17,28 +17,32 @@ include "basic_2/rt_transition/fpbc.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
-inductive fsb: relation3 genv lenv term ≝
-| fsb_intro: ∀G1,L1,T1.
-             (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → fsb G2 L2 T2) →
-             fsb G1 L1 T1
-.
+definition fsb: relation3 genv lenv term ≝
+           SN3 … fpb (feqg sfull).
 
 interpretation
   "strong normalization for parallel rst-transition (closure)"
   'PRedSubTyStrong G L T = (fsb G L T).
 
+(* Basic properties *********************************************************)
+
+lemma fsb_intro (G1) (L1) (T1):
+      (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫) → ≥𝐒 ❪G1,L1,T1❫.
+/5 width=1 by fpbc_intro, SN3_intro/ qed.
+
 (* Basic eliminators ********************************************************)
 
 (* Note: eliminator with shorter ground hypothesis *)
-(* Note: to be named fsb_ind when fsb becomes a definition like csx, rsx ****)
-lemma fsb_ind_alt (Q:relation3 …):
+lemma fsb_ind (Q:relation3 …):
       (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
         (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
         Q G1 L1 T1
       ) →
       ∀G,L,T. ≥𝐒 ❪G,L,T❫ → Q G L T.
 #Q #IH #G #L #T #H elim H -G -L -T
-/4 width=1 by fsb_intro/
+#G1 #L1 #T1 #H1 #IH1
+@IH -IH [ /4 width=1 by SN3_intro/ ] -H1 #G2 #L2 #T2 #H
+elim (fpbc_inv_gen sfull … H) -H #H12 #Hn12 /3 width=1 by/
 qed-.
 
 (* Basic_2A1: removed theorems 6: